First, recall that, as in Grünbaum's work [1]}, a general fourth order differential operator in \(K[\partial ]\)  can be given by
\(\left(\partial ^2 +\dfrac{c_2 }{2}\right)^2+2c_1 \partial +c_1^{\prime } +c_0 , \qquad \text{with}\quad c_0 , c_1 , c_2 \in K ,\) 
